Properties

Label 446400.lx
Number of curves $6$
Conductor $446400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("446400.lx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 446400.lx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
446400.lx1 446400lx6 [0, 0, 0, -4428288300, -113423212798000] [2] 150994944  
446400.lx2 446400lx4 [0, 0, 0, -276768300, -1772233918000] [2, 2] 75497472  
446400.lx3 446400lx5 [0, 0, 0, -272448300, -1830234238000] [2] 150994944  
446400.lx4 446400lx3 [0, 0, 0, -53280300, 116709698000] [2] 75497472 \(\Gamma_0(N)\)-optimal*
446400.lx5 446400lx2 [0, 0, 0, -17568300, -26781118000] [2, 2] 37748736 \(\Gamma_0(N)\)-optimal*
446400.lx6 446400lx1 [0, 0, 0, 863700, -1750462000] [2] 18874368 \(\Gamma_0(N)\)-optimal*
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 446400.lx6.

Rank

sage: E.rank()
 

The elliptic curves in class 446400.lx have rank \(0\).

Modular form 446400.2.a.lx

sage: E.q_eigenform(10)
 
\( q + 4q^{11} + 6q^{13} + 2q^{17} + 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.